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Vector Algebra question

2025 · 29 Jan · Shift 1 · Q39

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JEE Main
Mathematics
Vector Algebra
2025 · 29 Jan · Shift 1 · Q39

Vector Algebra question

2025 · 29 Jan · Shift 1 · Q39

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\vec{a}=\hat{i}+2 \hat{j}+\hat{k}

and

\vec{b}=2 \hat{i}+7 \hat{j}+3 \hat{k}

. Let

\mathrm{L}_1 : \overrightarrow{\mathrm{r}}=(-\hat{i}+2 \hat{j}+\hat{k})+\lambda \vec{a}, \mathrm{\lambda} \in \mathbf{R}

and

\mathrm{L}_2: \overrightarrow{\mathrm{r}}=(\hat{j}+\hat{k})+\mu \vec{b}, \mu \in \mathrm{R}

be two lines. If the line

\mathrm{L}_3

passes through the point of intersection of

\mathrm{L}_1

and

L_y

and is parallel to

\vec{a}+\vec{b}

, then

L_3

passes through the point :

A
$(-1, -1, 1)$
B
$(2, 8, 5)$
C
$(8, 26, 12)$
D
$(5, 17, 4)$

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